A cleaning device of this type is known from U.S. Pat. No. 7,013,528 B2. The previously known cleaning device consists of a base body to which a rotatable brush roller driven by an electric motor is attached, said roller transporting the dirt which is picked up into a dirt container arranged behind the brush roller. The brush roller picks up coarse dirt, which is picked up and retained by the dirt container. Fine dirt, in particular dust, can pass through the brush roller and is picked up by the cleaning cloth, which is arranged behind said roller and is attached to a cloth holder. This improves the cleaning effect compared to a cleaning device comprising merely a brush roller. However, the cloth holder is foldable and is rigidly connected to the base body, in such a way that the cloth holder engages with the floor to be cleaned even when said floor is rather obstructive, as is the case when cleaning carpeted floors for example. In this case, the cloth holder makes the cleaning operation more difficult because of the high friction.